Differential Equation Tapestries

Description: The infamous and very useful equation to move from contour integral to surface integral, also known as Stokes theorem.

Description: A science and mathematics visual featuring a differential equation, 'v dv/dx = -ω²x', above a graph of a sine wave with axes labeled 'y', '+A', '-A', '0', 'π/2', 'π', '3π/2', '2π', and 'ωt x'. To the right is a polar coordinate grid with concentric circles and radial lines, showing a segment of a circle and the label 'ωt'. The entire composition is in white on a black background.

Description: A scientific visual presentation with three main sections. The top displays a differential equation: 'dv/dt = d²x/dt² = -ω²x'. The middle shows a graph of x(t) versus time t, illustrating a sinusoidal wave from -A to +A, marked with π/2, π, 3π/2, and 2π. The right exhibits a circular diagram representing circular motion with axes labeled x and V, a point on the circle, and angles indicated by 'ωt'.

Description: The Jacobian matrix made out of the different partial derivatives of the components of the function, which is used in solving linear partial differential equations, and other problems in mathematics

Description: The infamous and very useful equation to move from volume integral to surface integral.

Description: In the late 18th century, Scottish physicist James Clerk Maxwell produced a set of equations that form the basis of the electromagnetic field. Maxwell's equations are important because they provide the foundation for modern physics.

Description: In the late 18th century, Scottish physicist James Clerk Maxwell produced a set of equations that form the basis of the electromagnetic field. Maxwell's equations are important because they provide the foundation for modern physics.

Description: The simple differential equation modeling the RLC circuit made of a capacitor, an inductor and a resistor without a generator.

Description: Faraday law of electromagnetic induction which is the founding block of almost all the engineering we use, from electrical to mechanical engineering.

Description: Merry Newtonmas

Description: Deriving d'Alembert wave equation of electric field from Maxwell's equations.

Description: The famous formula of radioactive decay, that has numerous applications, from medicine, to learning about the history of Earth and understanding the universe.